SOLUTION: The windows to a Tudor-style home create many types of quadrilaterals. Use the picture of the window below to answer the following questions. Picture: https://api.agilixbuzz.c

Question 1116959: The windows to a Tudor-style home create many types of quadrilaterals. Use the picture of the window below to answer the following questions.
Picture: https://api.agilixbuzz.com/Resz/~zd4LEAAAAAA_72Hj5cGAJA.pveOHg9l9atTB7D4K-3HOB/48780742,5C4,0,0/Assets/Media/Images/41.6-HOT4-TudorWindow.jpg
a. Determine which type of quadrilaterals you see. Name these quadrilaterals using the labeled vertices.
b. What properties of quadrilaterals would you have to know to identify the parallelograms in the picture? Be specific as to each type of parallelogram by using the properties between sides, angles, or diagonals for each.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
This is what I see at the link
There are right angles marked with little squares at E and F.
I believe those are not to be counted as quadrilaterals.
Those markings tell me that lines CE and DF are parallel.
I also believe there are facts to be assumed because of what the drawing looks like.
Lines assumed to be parallel:
AB||CD||EF (I would call those lines horizontal),
GH||AE||BF||JK (I would call those lines vertical),
GC||EB||OD (one set of"slanted" parallel lines),
DK||EF||CO (another set of"slanted" parallel lines not parallel those on the set above).
Lines assumed not to be parallel to any other line:
AI and BJ .
Line segments assumed congruent/lengths assumed to be equal:
EC=AC , GE=EO=OF=FK .

a.
I see some quadrilaterals without parallel sides.
AFGI and BJKE have no pair of parallel sides.
In some countries they call them trapezoids, but in the USA such a figure may be called a trapezium.
I see some quadrilaterals with only one pair parallel sides. They are not parallelograms.
AEGI, ACGH, BFKJ, AFGH, BEGH, CDFG, CDKE, CDKG (with parallel "horizontal" sides),
HACG, ACGI, BFKJ, BDKJ (with parallel "vertical" sides),
CGEM, NOEL, BDOE, BDOM,
DKFN, AFOC, ALMC, ANOC, AFOC, LNOC, LFOM
Because I live in the USA now, I will call them trapezoids, but in some countries such a quadrilateral would be called a trapezium, as my fourth grade teacher did.
I see parallelograms, that have two pairs of parallel sides.
Some of those parallelograms have 4 right angles, with two parallel "horizontal" sides that are perpendicular to the other two "vertical" sides.
AEGH, ABFE, ABDC, and CDEF are rectangles.
If there was a line segment LO,
quadrilateral CLOE, would have a pair of parallel sides with the same length
(CL and EO), perpendicular to side CE. That makes CLOE a rectangle, and CE=LO.
That makes DFOL also a rectangle, and one congruent (identical) to CLOE.
Because the diagonals of rectangles are equally long and bisect each other,
that makes CM=MO=LM=ME=LN=NF=DM=NO.
Some of the parallelograms in the figure are rhombi, with four congruent sides.
LNOM is a rhombus because it is a parallelogram, and LM=MO=LN=NO.
Some of the parallelograms in the figure are neither rectangles nor rhombi.
In this figure the parallelograms in the figure are neither rectangles nor rhombi have one pair of parallel sides that are "horizontal" and another pair of parallel sides that are slanted.
Examples of this are
CLEG, CDOG, CLFO, and LDKF.
There would be other quadrilateral that could be named if all the vertices were labeled.
b. Properties of quadrilaterals
The definition of trapezium or trapezoid are different in different countries.
In the USA, a trapezoid is defined as a quadrilateral with only one pair of parallel sides.
Some other countries use the British definition, where the names the reverse of the USA names.
and a trapezium is defined as a quadrilateral with no pair of parallel sides
A definition of parallelogram is a quadrilateral where pairs of opposite sides are parallel. (That can be considered a property).
As a consequence of that,
opposite sides are congruent (equal in length),
opposite angles are congruent (equal in measure), and
diagonals bisect each other.
A definition of rectangle is a parallelogram with one right angle.
As a consequence, a rectangle has all the properties of parallelograms,
it had four right angles, and its diagonals are equal in length.
A definition of rhombus is a parallelogram with four sides equal in length.
As a consequence, a rhombus has all the properties of parallelograms,
and its diagonal are perpendicular to each other.

Some of the properties listed above were used to name and classify quadrilaterals in the figure,
along with the assumptions about parallel lines and equally long segments listed at top.
RELATED QUESTIONS
what are all the different types of quadrilaterals and all the definitions of each... (answered by grishma.kshatriya)

Below was a school assessment question: "There are two windows in Elana's bedroom,... (answered by MathLover1)

Sam has 15 identical rectangular windows in his home. The length of each window is twice... (answered by Cromlix)

A rectangular picture window is 5 ft by 8 ft. Polly wants to put a trim molding around... (answered by 303795)

A house has 3 windows that are polygons with a total of 13 sides. Two of the windows are... (answered by macston)

The windows of a downtown office building are arranged so that each floor has six fewer... (answered by ikleyn,math_tutor2020)

a window washer can wash the windows on one side of a building in 112 working hours.with... (answered by stanbon)

A manufacturer of window frames knows from past experience that 10 per cent of the... (answered by Boreal)

A manufacturer of window frames knows from past experience that 20 per cent of the... (answered by stanbon)